Shirudo--welcome to japan!
I'll make a few comments here, but keep in mind that I'm not a even a beginner tax guru, and that as a long timer my situation is pretty remote from yours. Take anything I write as prefaced with "I think" or "From what I know (or have read").
First, the NTA document is not clear. Many are not, tho some are. One difficulty with NTA stuff is that you might find something that almost applies, and then mentally try to apply it to the situation at hand--so it then doesn't look clear. OTOH, sometimes the NTA docs look very clear--when you've found something that directly applies. So bracket that for the time being.
Generally, I'd say you're working here, so you're liable for tax. Even first year english teachers pay taxes their first year (many start in april of the year concerned). However (and this is a big one), there are two general taxes, national and local. National is what you'd expect, local (more commonly: residence tax) is paid to the city (or locality) where you live. IMO, you will need to file a tax return soon (national), and will then have to pay something (or not) depending on 2020 (whether and how much withholding, maybe any dependents, and so on.
Local/residence tax is different. It is paid in arrears, and you almost never file a return for this--it is based on your previous year's national tax return (so there is a one year delay). Also, for local/residence tax, where you pay and who you owe is generally determined by where you live on january 1st of a given year. >>Since you were not in japan on january 1st, 2020, I don't think you will owe residence tax for that year. (This will save you about 10%.) Residence tax is based on your national return, and after you've done your national tax filing, that info (mid-spring) is relayed to the city office where you live, and they calculate/assess the residence tax. This assessment then gets sent to residents in late june or so, and you then start paying--either via deductions from your ongoing salary (if a regular employee here), or via a set of bills mailed to you (installments), which you'd need to pay at a bank. The thing to remember is that this tax is paid in arrears--when you pay these bills, they're for the previous year's taxes.
Back to national taxes. Again, tho you're working remotely, you've been doing that work while located in japan, so you'll need to file and pay. Filing is generally easy here (certainly much easier than in the US!), and locals can now even do it using a phone. But while the tax office is typically quite helpful here (and they're not out to screw you), language may be a problem--in my experience english speakers are generally unavailable, or hard to get to. The tax office can also be pretty busy during tax filing time (take a number and sit and wait). You might consider using a local tax preparer--or course one who is familiar with situations such as yours. The preparer would do your tax return and submit it for you.
Okay, that's my attempt at this--it's still early and time for some more coffee!
Last, another good source of info on this would be this reddit sub:
https://www.reddit.com/r/japanlife/ There are a couple of people there that might offer excellent tax info. But the moderators there can sometimes flag a new user's posts (not enough 'karma', so a post might be deleted as spam). If you have used reddit some, it should be okay, but if you're starting a new account, it might take a post or few, or maybe message the moderators, who will then let your post go thru.
